The mass has to do with it retaining an atmosphere, and an active core would have to do with it producing more atmosphere through volcanic eruptions.
The magnetic core primarily creates the magnetosphere which in turn creates the Van Allen Radiation belts, shielding us from harmful radiation, and it also redirects charged particles to the N and S poles (Auroras). I haven't seen any correlation between a magnetic core and retaining an atmosphere in my readings.
-SW